Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. Dic356 | C16 | semidirect |
| 68. C89 | #7069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic356 | 2 |
| #26018322 | 2 |
| C8×C16×C89 | 2 |
| #7069 | 89 |